Multi-objective ant colony optimization based on decomposition for bi-objective traveling salesman problems

This paper proposes a framework named multi-objective ant colony optimization based on decomposition (MoACO/D) to solve bi-objective traveling salesman problems (bTSPs). In the framework, a bTSP is first decomposed into a number of scalar optimization subproblems using Tchebycheff approach. To suit for decomposition, an ant colony is divided into many subcolonies in an overlapped manner, each of which is for one subproblem. Then each subcolony independently optimizes its corresponding subproblem using single-objective ant colony optimization algorithm and all subcolonies simultaneously work. During the iteration, each subproblem maintains an aggregated pheromone trail and an aggregated heuristic matrix. Each subcolony uses the information to solve its corresponding subproblem. After an iteration, a pheromone trail share procedure is evoked to realize the information share of those subproblems solved by common ants. Three MoACO algorithms designed by, respectively, combining MoACO/D with AS, MMAS and ACS are presented. Extensive experiments conducted on ten bTSPs with various complexities manifest that MoACO/D is both efficient and effective for solving bTSPs and the ACS version of MoACO/D outperforms three well-known MoACO algorithms on large bTSPs according to several performance measures and median attainment surfaces.